Hyperplane, any clear explaination?

**ibrex77** · May 13th 2010, 02:19 PM

Hi math guys,

I am happy to join you in this forum (I also like the fractal symbol)

. My math background is not that good

, that is why I am looking for clear explanation (examples, figures,...etc) rather than equations and symbols

.
I have tried to understand the hyperplane and its relationship to the plane but I can't. I appreciate any help.

Best regards,

**Chris L T521** · May 13th 2010, 04:26 PM

Originally Posted by ibrex77

Hi math guys,

I am happy to join you in this forum (I also like the fractal symbol)

. My math background is not that good

, that is why I am looking for clear explanation (examples, figures,...etc) rather than equations and symbols

.
I have tried to understand the hyperplane and its relationship to the plane but I can't. I appreciate any help.

Best regards,

In a nutshell:

In $\mathbb{R}^2$ , a hyperplane is a line of the form $ax+by=c$ (note that this is the standard form of a line).

In $\mathbb{R}^3$ , a hyperplane is our ordinary plane of the form $ax+by+cz=d$ (note that this is the standard form of a plane).

Now, hyperplanes (in general) are planes in $\mathbb{R}^n$ . They are of the form $\sum_{i=1}^n a_ix_i=b\implies a_1x_1+a_2x_2+\ldots+a_nx_n=b$ .

Unfortunately, there is no real way to visualize these things in 4 or more dimensions!

Does this little bit make sense?

**ibrex77** · May 13th 2010, 06:32 PM

This is just what I am looking for. using line and plane which are somethings I already know

to define the hyperplane is really a great idea

.

Thank you again

.

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